Zika virus (ZIKV), an emerging flavivirus, has recently spread explosively through the Western hemisphere. In addition to symptoms including fever, rash, arthralgia, and conjunctivitis, ZIKV infection of pregnant women can cause microcephaly and other developmental abnormalities in the fetus. We report herein the results of ZIKV infection of adult rhesus macaques. Following subcutaneous infection, animals developed transient plasma viremia and viruria from 1–7 days post infection (dpi) that was accompanied by the development of a rash, fever and conjunctivitis. Animals produced a robust adaptive immune response to ZIKV, although systemic cytokine response was minimal. At 7 dpi, virus was detected in peripheral nervous tissue, multiple lymphoid tissues, joints, and the uterus of the necropsied animals. Notably, viral RNA persisted in neuronal, lymphoid and joint/muscle tissues and the male and female reproductive tissues through 28 to 35 dpi. The tropism and persistence of ZIKV in the peripheral nerves and reproductive tract may provide a mechanism of subsequent neuropathogenesis and sexual transmission. Although it was first identified almost 70 years ago, Zika virus had rarely been associated with pathology in humans until the 21st century. Recent outbreaks in the South Pacific and the Americas have been characterized by numerous confirmed cases, some involving neurologic sequelae and, of most concern, birth defects following infection of pregnant women. Here, we present the results of experimental infection of adult rhesus macaques with a strain of Zika virus isolated during the recent epidemic in the Western hemisphere. Following infection, Zika virus was detected in the sera and urine of all infected animals. Further, we detected virus in multiple tissues of infected animals as late as 35 days post infection, indicating viral persistence. The apparent tropism of the virus for tissues of the peripheral nervous system as well as the reproductive tracts of males and females has implications for the further characterization of the mechanism(s) of Zika virus pathogenesis. Additionally, this model provides a platform for development and testing of preventative or therapeutic interventions to combat the emergence of this virus.